## PRP Records

### Probable Primes Top 10000

#### (253476 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 8001 2^218680-719 65830 Yves Minet 05/2012 8002 18^52424+17 65807 Lelio R Paula 08/2013 8003 19062^2827+2827^19062 65790 Hans Havermann 08/2019 8004 (2*15683^15683+1)/732384425 65789 David Broadhurst 09/2010 8005 (23*2^218517+1)/19003 65778 Lelio R Paula 07/2012 8006 (5*10^65773+1)/3 65774 Erik Branger 12/2013 8007 160^29839-159 65769 Norbert Schneider 12/2018 8008 2^218457-17329 65763 Enzo Doria 05/2013 8009 151703#+223381 65759 Nicolas PALAU 10/2016 8010 2^218436+40755 65756 Lelio R Paula 10/2011 8011 2^218399-4627 65745 Yves Minet 05/2019 8012 (F(44)^7433-F(43)^7433)/F(42) 65744 Wayne Halsdorf 03/2012 8013 15952^13219+13219^15952 65742 Hans Havermann 08/2019 8014 157^29934+29934^157 65733 Serge Batalov 05/2014 8015 211^28273-2 65715 Lelio R Paula 09/2013 8016 (59*10^65712+31)/9 65713 Robert Price 09/2015 8017 611^23586+23586^611 65712 Norbert Schneider 08/2016 8018 p(13991)#/2+32 65712 Robert Price 12/2016 8019 15865^13864+13864^15865 65712 Hans Havermann 07/2019 8020 2^218282-18485 65710 Enzo Doria 05/2013 8021 2^218274-111251 65708 Enzo Doria 05/2014 8022 2*F(314335)-1 65693 Henri Lifchitz 12/2009 8023 2^218200+427 65685 Henri Lifchitz 01/2005 8024 (10199^16384+10197^16384)/2 65676 Jeppe Stig Nielsen 04/2018 8025 (10199^(2^14)+(10197)^(2^14))/2 65676 Robert Price 05/2018 8026 46532!3+3 65667 Robert Price 10/2014 8027 2^218120-147 65661 Lelio R Paula 08/2011 8028 452^24729+24729^452 65659 Norbert Schneider 09/2016 8029 5817^17440+17440^5817 65657 Norbert Schneider 06/2019 8030 2^218102-114893 65656 Enzo Doria 05/2015 8031 (15*2^218083-1)/17 65650 Lelio R Paula 01/2014 8032 (15*2^218081+1)/18941 65646 Lelio R Paula 08/2012 8033 15818^14115+14115^15818 65640 Hans Havermann 08/2019 8034 (306^26407-1)/305 65638 Eric Chen 09/2017 8035 19^51326+36 65634 Lelio R Paula 08/2013 8036 (21*2^218045-1)/451583 65634 Lelio R Paula 01/2014 8037 2^217989-33 65622 Lelio R Paula 08/2011 8038 (13*2^217961+1)/3 65614 Lelio R Paula 06/2012 8039 4*6^84315-5 65611 Lelio R Paula 09/2014 8040 (315047^11933+1)/315048 65607 Faysal YAtim 06/2008 8041 6^84303+55 65601 Lelio R Paula 07/2013 8042 16585^9024+9024^16585 65601 Hans Havermann 08/2019 8043 18462^3575+3575^18462 65601 Hans Havermann 08/2019 8044 15963^12862+12862^15963 65597 Hans Havermann 08/2019 8045 (-lucasV(1,2,435857)+2)/(173*859*8017) 65595 Mike Oakes 04/2017 8046 (9787*2^217873-1)/37 65589 Lelio R Paula 04/2015 8047 5*2^217858+3 65583 Lelio R Paula 04/2014 8048 (19*10^65572+119)/3 65573 Robert Price 02/2017 8050 20^50399+51 65571 Lelio R Paula 08/2013 8049 7162^17009+17009^7162 65571 Norbert Schneider 07/2018 8051 11^62946-5670 65552 Enzo Doria 01/2013 8052 2^217742-3911 65547 Yves Minet 08/2009 8053 (19*10^65545+77)/3 65546 Robert Price 08/2016 8054 2^217731+131 65544 Lelio R Paula 08/2011 8055 2^217720-111287 65541 Enzo Doria 05/2014 8056 (365^25579+1)/366 65539 Eric Chen 10/2017 8057 10^65537+27 65538 Robert Price 01/2011 8058 10^65537-76859 65537 Patrick De Geest 05/2013 8059 (28*10^65532+359)/9 65533 Robert Price 11/2017 8060 (10223*2^217676+1)/3 65531 Lelio R Paula 06/2014 8061 PadovanNumber[536485] 65518 Eric W. Weisstein 05/2009 8062 5*10^65509+23 65510 Robert Price 11/2017 8063 (8*10^65507-83)/3 65508 Robert Price 10/2017 8064 7*10^65492-47 65493 Robert Price 02/2017 8065 2^217547-1868407 65489 Enzo Doria 04/2016 8066 2^217531-111769 65484 Enzo Doria 05/2014 8067 7^77484-18 65482 Lelio R Paula 06/2013 8068 5754^17413+17413^5754 65473 Norbert Schneider 05/2019 8069 2^217488-113285 65471 Enzo Doria 07/2014 8070 151153#/30-30 65468 Henri Lifchitz 12/2011 8071 2^217466+4257 65464 Lelio R Paula 10/2011 8072 46396!3-81 65455 Robert Price 09/2014 8073 2^217421-113185 65451 Enzo Doria 07/2014 8074 (6883*2^217440-1)/1061193295893 65448 Lelio R Paula 04/2015 8075 2^217408-2145 65447 Lelio R Paula 10/2011 8076 2^217398-16947 65444 Enzo Doria 05/2013 8077 16097^11628+11628^16097 65443 Hans Havermann 07/2019 8078 8*5^93613+3 65434 Lelio R Paula 09/2014 8079 15929^12810+12810^15929 65430 Hans Havermann 07/2019 8080 11^62828-5310 65429 Enzo Doria 01/2013 8081 10^65426+13 65427 Robert Price 01/2011 8082 2^217341-6555 65427 Lelio R Paula 10/2011 8083 10^65426-54849 65426 Patrick De Geest 05/2013 8084 (21*2^217363-1)/56003626667 65424 Lelio R Paula 01/2014 8085 30011^14608-108 65405 Enzo Doria 07/2012 8086 119^31504-2 65389 Lelio R Paula 10/2017 8087 (43^40031-1)/42 65388 Robert Price 04/2014 8088 2^217190+94395 65381 Henri Lifchitz 02/2005 8089 15^55587+46 65376 Lelio R Paula 08/2013 8090 18443^3502+3502^18443 65368 Hans Havermann 07/2019 8091 2^217088-111833 65350 Enzo Doria 05/2014 8092 (13*2^217069-1)/1682945 65340 Lelio R Paula 01/2014 8093 (10^65340+47)/3 65340 Robert Price 11/2017 8094 (62*10^65331+1)/9 65332 Serge Batalov 11/2010 8095 2^216947-111351 65308 Enzo Doria 05/2014 8096 -E(18022)/775201845682685322943949235068359 65307 Thomas Ritschel 02/2017 8097 (13*10^65297+83)/3 65298 Robert Price 09/2016 8098 16413^9502+9502^16413 65288 Hans Havermann 07/2019 8099 5^93400-8 65284 Lelio R Paula 06/2013 8100 2^216802-165 65264 Lelio R Paula 08/2011 8101 2^216799-28635 65264 Lelio R Paula 10/2011 8102 5*10^65255+51 65256 Robert Price 01/2017 8103 2^216762-167 65252 Lelio R Paula 08/2011 8104 11^62657-5790 65251 Enzo Doria 01/2013 8105 3^136756-112880 65250 Enzo Doria 06/2014 8106 2^216752+21 65249 Lelio R Paula 08/2011 8107 3*10^65247+11 65248 Robert Price 11/2017 8108 11^62651-2700 65245 Enzo Doria 12/2012 8109 15130^15609-15609^15130 65244 Norbert Schneider 07/2018 8110 Pell-LucasQ(170413)/2 65230 Eric W. Weisstein 12/2006 8111 gcd(V(790525),5*F(158105)*(F(158105)+1)+1) 65230 Serge Batalov 04/2015 8112 (2^216676-1017)/637 65224 Lelio R Paula 04/2012 8113 2^216652-2327 65219 Yves Minet 10/2013 8114 (9179*2^216648-1)/4667 65218 Lelio R Paula 04/2015 8115 (5*10^65203-119)/3 65204 Robert Price 04/2016 8116 15977^12034+12034^15977 65193 Hans Havermann 07/2019 8117 2^216555-113269 65190 Enzo Doria 07/2014 8119 (9513^16384+1)/2 65181 Henri Lifchitz 02/2007 8118 15753^13730+13730^15753 65181 Hans Havermann 07/2019 8120 2^216474+12915 65166 Lelio R Paula 02/2013 8121 19^50958-32 65163 Lelio R Paula 08/2013 8122 2^216442-112133 65156 Enzo Doria 06/2014 8123 2^216437-112213 65155 Enzo Doria 06/2014 8124 2^216435-112767 65154 Enzo Doria 06/2014 8125 2^216420+12705 65149 Lelio R Paula 02/2013 8126 8*3^136507-7 65132 Lelio R Paula 04/2014 8127 (-lucasV(1,2,432719)-2)/(5*461) 65128 Mike Oakes 03/2017 8128 16803^7496+7496^16803 65109 Hans Havermann 07/2019 8129 15132^15575-15575^15132 65102 Norbert Schneider 07/2018 8130 5*10^65086-51 65087 Robert Price 10/2017 8131 2^216197-111769 65082 Enzo Doria 05/2014 8132 6^83631-79 65078 Lelio R Paula 07/2013 8133 572^23601+23601^572 65078 Norbert Schneider 08/2016 8135 (3^136399-7)/544220 65074 Lelio R Paula 04/2012 8134 15592^14911+14911^15592 65074 Hans Havermann 07/2019 8136 2^216154-1421 65069 Yves Minet 01/2013 8137 2^216145-112663 65067 Enzo Doria 06/2014 8138 (7*10^65064+53)/3 65065 Robert Price 10/2017 8139 132013*10^65050+2^216091-1 65056 Gilbert Mozzo 01/2014 8140 132019*10^65050+2^216091-1 65056 Gilbert Mozzo 01/2014 8141 148918*10^65050+2^216091-1 65056 Gilbert Mozzo 02/2014 8142 194014*10^65050+2^216091-1 65056 Gilbert Mozzo 02/2014 8143 223864*10^65050+2^216091-1 65056 Gilbert Mozzo 04/2014 8146 82090*10^65050+2^216091-1 65055 Gilbert Mozzo 07/2012 8145 95133*10^65050+2^216091-1 65055 Gilbert Mozzo 12/2013 8144 98142*10^65050+2^216091-1 65055 Gilbert Mozzo 12/2013 8147 ((2^216091-1)*34009-48)/25 65054 Serge Batalov 01/2012 8148 5977*10^65050+2^216091-1 65054 Gilbert Mozzo 03/2012 8149 7*2^216091+2^298-13 65051 Peter Lesala 03/2007 8150 2^216091+2*29208-1 65050 Makoto Morimoto 10/2013 8151 15845^12736+12736^15845 65045 Hans Havermann 07/2019 8152 (10^(2*32521+1)-6*10^32521-1)/3 65043 Robert Price 02/2016 8153 p(13861)#/2+256 65039 Robert Price 05/2017 8154 (2^216091-2096)/(2^4*3*2918437*5220283) 65036 Makoto Morimoto 10/2017 8155 11^62439-4380 65024 Enzo Doria 01/2013 8156 16489^8776+8776^16489 65022 Hans Havermann 07/2019 8157 3^136244+2 65005 Mike Oakes 11/2009 8158 13^58343-50 64991 Lelio R Paula 07/2013 8159 331^25791-10002 64989 Enzo Doria 07/2012 8160 2^215877+131 64986 Lelio R Paula 08/2011 8161 4*5^92959+9 64977 Lelio R Paula 09/2014 8162 2^215789-18825 64959 Lelio R Paula 09/2011 8163 (2^215801-509203)/41327 64958 Lelio R Paula 05/2012 8164 U(315311) 64954 Serge Batalov 03/2015 8165 46072!3-59049 64951 Robert Price 12/2015 8166 2^215750-5955 64948 Lelio R Paula 09/2011 8167 13^58281+46 64922 Lelio R Paula 07/2013 8168 15633^14212+14212^15633 64919 Hans Havermann 07/2019 8169 2^215623+183 64909 Lelio R Paula 08/2011 8170 (46*10^64904+521)/9 64905 Robert Price 08/2017 8171 (3^136043-2^136043)/(19862279*33466579) 64895 Mike Oakes 12/2016 8172 5*2^215554+3 64889 Lelio R Paula 04/2014 8173 2^215541-112075 64885 Enzo Doria 06/2014 8174 2*10^64882-3 64883 Dmitry Domanov 11/2010 8175 16592^8121+8121^16592 64869 Hans Havermann 07/2019 8176 10^64862+342339 64863 Patrick De Geest 05/2013 8177 10^64862-47 64862 Robert Price 05/2011 8178 19^50718-84 64856 Lelio R Paula 08/2013 8179 (3045*2^215471-1)/(17*1151*27067*173473) 64853 Jens K. Andersen 09/2007 8180 86413!6-12 64846 Robert Price 08/2018 8181 10^64843+4278697839 64844 Robert Price 05/2015 8182 10^64843+21967 64844 Patrick De Geest 03/2016 8183 10^64843-340073 64843 Patrick De Geest 03/2016 8184 11^62254+70 64831 Lelio R Paula 07/2013 8185 2^215351-111925 64828 Enzo Doria 05/2014 8186 2^215310-117 64815 Lelio R Paula 08/2011 8187 124^30958-123 64809 Norbert Schneider 02/2015 8188 (7*10^64807+17)/3 64808 Erik Branger 03/2014 8189 (7*10^(2*32400+1)-27*10^32400-7)/9 64801 Robert Price 11/2015 8190 2^215243-15949 64795 Enzo Doria 04/2013 8191 23^47581-22^47581 64793 Robert Price 08/2012 8192 (62*10^64783-17)/9 64784 Robert Price 09/2015 8193 5*3^135747-4 64769 Lelio R Paula 04/2014 8194 (59*10^64767-41)/9 64768 Robert Price 09/2015 8196 (2^215140+3)/19 64763 Lelio R Paula 04/2012 8195 2^215135-17169 64763 Enzo Doria 05/2013 8197 16078^10665+10665^16078 64762 Hans Havermann 07/2019 8198 2^215115-111277 64757 Enzo Doria 05/2014 8199 9*5^92641+2 64755 Lelio R Paula 09/2014 8200 (lucasV(1,2,430086)-2)/(7*1033) 64731 Mike Oakes 03/2017 8201 5791^17200+17200^5791 64720 Norbert Schneider 12/2018 8202 (5*10^64715-23)/9 64715 Robert Price 11/2014 8203 2^214938-1781 64703 Yves Minet 03/2013 8204 21003^1202+1202^21003 64688 Hans Havermann 07/2019 8205 11^62111-420 64682 Enzo Doria 08/2012 8206 18870^2677+2677^18870 64680 Hans Havermann 07/2019 8207 5^92525+42 64673 Lelio R Paula 06/2013 8208 2^214824+71893 64669 Enzo Doria 04/2016 8209 19157^2374+2374^19157 64665 Hans Havermann 08/2019 8210 2^214799-2221 64661 Yves Minet 08/2013 8211 18393^3274+3274^18393 64653 Hans Havermann 07/2019 8212 5939^17128+17128^5939 64637 Norbert Schneider 10/2018 8213 (21*2^214688+1)/293 64627 Lelio R Paula 08/2012 8214 92^32907+32907^92 64623 Serge Batalov 05/2014 8215 17650^4579+4579^17650 64613 Hans Havermann 07/2019 8216 (89*10^64608-539)/9 64609 Robert Price 11/2017 8217 6^83013+101 64597 Lelio R Paula 07/2013 8218 p(13775)#/2+8 64594 Robert Price 01/2017 8219 (7*10^64568-43)/9 64568 Robert Price 10/2014 8220 Pell-LucasQ(168677)/2 64566 Eric W. Weisstein 11/2006 8221 (24737*2^214476+1)/2877 64565 Lelio R Paula 06/2014 8222 (47*2^214463+1)/7 64561 Lelio R Paula 04/2015 8223 2^214458+54615 64559 Lelio R Paula 10/2011 8224 (3^135322+7)/122911408 64557 Lelio R Paula 04/2012 8225 2^214389-683113 64538 Paul Bourdelais 03/2013 8226 (76*10^64534+113)/9 64535 Robert Price 11/2017 8227 2^214369-111241 64532 Enzo Doria 05/2014 8228 (19^50461+3^50461)/22 64526 Robert Price 07/2013 8229 11^61954-3660 64519 Enzo Doria 12/2012 8230 (23*2^214319-1)/21 64517 Lelio R Paula 01/2014 8231 (58695*2^214310-1)/571 64516 Lelio R Paula 04/2015 8232 2^214300-4547 64511 Yves Minet 03/2019 8233 35^41779-34 64510 Norbert Schneider 04/2014 8234 (159^29303+1)/160 64506 Eric Chen 12/2017 8235 (89*10^64504-179)/9 64505 Robert Price 11/2017 8236 11^61939-5220 64503 Enzo Doria 01/2013 8237 (2^214271+78557)/35 64501 Lelio R Paula 05/2012 8238 L(308604)+P(308604) 64495 Robert Price 12/2017 8239 126^30706-125 64494 Norbert Schneider 02/2015 8240 gcd(V(1157265),5*F(231453)*(F(231453)-1)+1) 64492 Serge Batalov 04/2015 8241 2^214215+12909 64486 Lelio R Paula 10/2011 8242 16581^7738+7738^16581 64478 Hans Havermann 07/2019 8243 5^92225+66 64463 Lelio R Paula 06/2013 8244 2^214126-240551 64459 Paul Bourdelais 03/2013 8245 8*6^82827+5 64453 Lelio R Paula 09/2014 8246 (31*2^214120-1)/2170485 64452 Lelio R Paula 01/2014 8247 (31*2^214088-1)/5955 64445 Lelio R Paula 01/2014 8248 14^56227+89 64444 Lelio R Paula 08/2013 8249 10^64436+2667 64437 Patrick De Geest 05/2013 8250 65^35543-64^35543 64437 Robert Price 08/2013

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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